Consider following return series of two stocks, A and B

Stock A	Stock B
2.0%	12.5%
5.1%	-9.2%
5.5%	8.7%
7.3%	10.4%
6.2%	-7.2%
13.0%	-9.6%
1.2%	-5.4%
-7.0%	21.0%
5.5%	12.4%
-10.0%	-15.0%
3.2%	35.7%
19.0%	-14.2%
1.0%	27.9%
3.0%	16.5%
7.1%	6.6%

A. What are the asset allocation percentages of stock A, B, and risk-free asset in the complete portfolio if the investor is seeking 4.5% return on his/her complete portfolio? What is the Sharpe Ratio of optimal risky portfolio? Assume that the prevailing rate on risk-free asset is 25%.

(hint: use geometric return for optimal risky portfolio weight calculation)

B. Suppose another asset, stock C, becomes available with expected return of 7% with standard deviation of 10%. If you were to generate new optimal risky portfolio using stock C, what is the new percentage allocations of stock A, B, and C in the new portfolio? What is the new Sharpe ratio of optimal risky portfolio?

(hint: treat old optimal risky portfolio as a single stock)

C. Suppose you are investing $100,000 into above mentioned new optimal risky portfolio only. You were sure to deliver the predicted return until 2020 came and pandemic hit. To protect your portfolio position, you have found a counterparty who is willing to write a Over-The-Counter put option for your portfolio for the next 1.5 years to come. You want to maintain total asset under management to be $95,000 or higher. In establishing this protective put position on your portfolio, what is the put premium that you need to pay to the counterparty? You assume that the Black-Scholes model holds while the predicted level of risk (i.e. standard deviation of optimal risky portfolio) has doubled, no continuous dividend is paid, and prevailing risk-free rate is 2%.